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About the book

Description

This book consists of the lecture notes, problems and solutions from the author’s Coursera course “Fibonacci numbers and the golden ratio.” YouTube links to the course’s videos are provided at the top of each lecture. In these lectures, we learn the origin of the Fibonacci numbers and the golden ratio, and derive a formula to compute any Fibonacci number from powers of the golden ratio. We learn how to add a series of Fibonacci numbers and their squares, and unveil the mathematics behind a famous paradox called the Fibonacci bamboozlement. We construct a beautiful golden spiral and an even more beautiful Fibonacci spiral, and we learn why the Fibonacci numbers can appear unexpectedly in nature. At the end of each lecture, students are given interesting problems to solve, and the author’s detailed solutions are provided in the book’s Appendix.

Content

The Fibonacci sequence

The Fibonacci sequence redux

The golden ratio

Fibonacci numbers and the golden ratio

Binet’s formula

The Fibonacci Q-matrix

Cassini’s identity

The Fibonacci bamboozlement

Sum of Fibonacci numbers

Sum of Fibonacci numbers squared

The golden rectangle

Spiraling squares

The golden spiral

An inner golden rectangle

The Fibonacci spiral

Fibonacci numbers in nature

Continued fractions

The golden angle

The growth of a sunflower

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